Solve the Problem $\mathrm { A } = \left[ \begin{array} { r r r } 1 & - 3 & 0 \\ - 4 & 0 & 2 \\ 4 & 1 & - 2 \end{array} \right]$

question 75

Multiple Choice

Solve the problem.
-Let $\mathrm { A } = \left[ \begin{array} { r r r } 1 & - 3 & 0 \\ - 4 & 0 & 2 \\ 4 & 1 & - 2 \end{array} \right]$ and $\mathbf { b } = \left[ \begin{array} { r } 9 \\ - 6 \\ 4 \end{array} \right]$ .
Define a transformation $\mathrm { T }$ : $\mathfrak { R } ^ { 3 } \rightarrow \mathbb { R } ^ { 3 }$ by $\mathrm { T } ( \mathbf { x } ) = \mathrm { Ax }$ .
If possible, find a vector $x$ whose image under $\mathrm { T }$ is $\mathbf { b }$ . Otherwise, state that $\mathbf { b }$ is not in the range of the transformation $\mathrm { T }$ .

• A)
• \[\left[ \begin{array} { r }
• 3 \\
• - 2 \\
• 0
• \end{array} \right]\]
• B) \(\mathbf { b }\) is not in the range of the transformation \(T\).
• C) \(\left[ \begin{array} { r } 3 \\ 3 \\ - 2 \end{array} \right]\)
• D)
• \[\left[ \begin{array} { r }
• 3 \\
• - 2 \\
• 3
• \end{array} \right]\]

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